Generative neural image compression supports data representation with extremely low bitrate, allowing clients to synthesize details and consistently producing highly realistic images. By leveraging the similarities between quantization error and additive noise, diffusion-based generative image compression codecs can be built using a latent diffusion model to denoise'' the artifacts introduced by quantization. However, we identify three critical gaps in previous approaches following this paradigm~(namely, the noise level, noise type, and discretization gaps) that result in the quantized data falling out of the data distribution known by the diffusion model. In this work, we propose a novel quantization-based forward diffusion process with theoretical foundations that tackles all three aforementioned gaps. We achieve this through universal quantization with a carefully tailored quantization schedule and a diffusion model trained with uniform noise. Compared to previous work, our proposal produces consistently realistic and detailed reconstructions, even at very low bitrates. In such a regime, we achieve the best rate-distortion-realism performance, outperforming previous related works.